Questions: Solve for (x) (z=2x-3y)

Solution Steps

To solve for \( x \) in the equation \( z = 2x - 3y \), we need to isolate \( x \) on one side of the equation. This involves rearranging the equation by performing algebraic operations.

1. Add \( 3y \) to both sides of the equation to move the \( y \)-term to the left side.
2. Divide both sides by 2 to solve for \( x \).

Starting with the equation: \[ z = 2x - 3y \] we add \( 3y \) to both sides to isolate the term with \( x \): \[ z + 3y = 2x \]

Next, we divide both sides of the equation by 2 to solve for \( x \): \[ x = \frac{z + 3y}{2} \]

Given \( z = 10 \) and \( y = 2 \), we substitute these values into the equation: \[ x = \frac{10 + 3 \cdot 2}{2} \]

Simplify the expression to find the value of \( x \): \[ x = \frac{10 + 6}{2} = \frac{16}{2} = 8.0 \]

Final Answer